Airfoil shape for a compressor

ABSTRACT

An article of manufacture having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches. The profile sections at the Z distances can be joined smoothly with one another to form a complete airfoil shape.

BACKGROUND OF THE INVENTION

The present invention relates to airfoil, such as for a blade or vane ofa gas turbine (hereinafter either blade or vane for ease of descriptionand understanding). In particular, the invention relates to compressorairfoil profiles for a Stage 1 rotor vane.

In a gas turbine, many system requirements should be met at each stageof a gas turbine's flow path section to meet design goals. A turbine hotgas path requires that the compressor airfoil rotor vane meet designgoals and desired requirements of efficiency, reliability, and loading.For example, and in no way limiting of the invention, a vane of acompressor rotor should achieve thermal and mechanical operatingrequirements for that particular stage. Further, for example, and in noway limiting of the invention, a vane of a compressor rotor shouldachieve thermal and mechanical operating requirements for thatparticular stage.

Past efforts to meet design goals and desired requirements have providedcoatings on the airfoil, but the coatings may not be robust enough orpermanent to provide design goals and desired requirements. Accordingly,it is desirable to provide an airfoil configuration with a profile meetto design goals and desired requirements.

BRIEF DESCRIPTION OF THE INVENTION

In one embodiment of the invention, an article of manufacture comprisesa vane airfoil having an airfoil shape, the airfoil having a nominalprofile substantially in accordance with Cartesian coordinate values ofX, Y and Z set forth in TABLE A. X and Y are distances which, whenconnected by smooth continuing arcs, define airfoil profile sections ateach distance Z in inches. The profile sections at the Z distances arejoined smoothly with one another to form a complete airfoil shape.

In another embodiment according to the invention, a compressor vaneincludes a vane airfoil having an uncoated nominal airfoil profilesubstantially in accordance with Cartesian coordinate values of X, Y andZ set forth in TABLE A. X and Y are distances in inches which, whenconnected by smooth continuing arcs, define airfoil profile sections ateach Z distance in inches. The profile sections at the Z distances arejoined smoothly with one another to form a complete airfoil shape. X andY distances are scalable as a function of a constant to provide ascaled-up or scaled-down airfoil.

In a further embodiment of the invention, a compressor comprises acompressor wheel having a plurality of blades cooperating with rotorvanes. Each of the vanes includes an airfoil having an airfoil shape.The airfoil comprises a nominal profile substantially in accordance withCartesian coordinate values of X, Y and Z set forth in TABLE A. X and Yare distances in inches which, when connected by smooth continuing arcs,define the airfoil profile sections at each distance Z in inches. Theprofile sections at the Z distances are joined smoothly with one anotherto form a complete airfoil shape.

In a yet further embodiment of the invention, a compressor comprises acompressor wheel having a plurality of blades cooperating with rotorvanes, and each of the vanes include an airfoil having an uncoatednominal airfoil profile substantially in accordance with Cartesiancoordinate values of X, Y and Z set forth in TABLE A. X and Y aredistances which, when connected by smooth continuing arcs, defineairfoil profile sections at each distance Z in inches. The profilesections at the Z distances are joined smoothly with one another to forma complete airfoil shape. The X, Y and Z distances are scalable as afunction of a constant to provide a scaled-up or scaled-down vaneairfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a fragmentary cross-sectional view of a compressorillustrating various stages of the compressor, as embodied by theinvention;

FIG. 2 is perspective view of a blade for a compressor, as embodied bythe invention;

FIG. 3 is a side elevational view thereof;

FIG. 4 is a tangential and rear perspective view of a compressor blade,as embodied by the invention;

FIG. 5 is a end view of a compressor blade as viewed looking radiallyoutwardly from the blade tip, as embodied by the invention;

FIG. 6 is a view similar to FIG. 2; and

FIG. 7 is a cross-sectional view thereof taken generally about on line7-7 in FIG. 6.

DETAILED DESCRIPTION OF THE INVENTION

In accordance with one embodiment of the instant invention, an articleof manufacture has a nominal profile substantially in accordance withCartesian coordinate values of X, Y and Z set forth in TABLE A, andwherein X and Y are distances in inches which, when connected by smoothcontinuing arcs, define airfoil profile sections at each distance Z ininches, the profile sections at the Z distances being joined smoothlywith one another to form a complete airfoil shape.

In accordance with one embodiment of the instant invention, there isprovided an airfoil compressor shape for a vane of a gas turbine thatenhances the performance of the gas turbine. The airfoil shape hereofalso improves the interaction between various stages of the compressorand affords improved aerodynamic efficiency, while simultaneouslyreducing stage airfoil thermal and mechanical stresses.

The vane airfoil profile, as embodied by the invention, is defined by aunique loci of points to achieve the necessary efficiency and loadingrequirements whereby improved compressor performance is obtained. Theseunique loci of points define the nominal airfoil profile and areidentified by the X, Y and Z Cartesian coordinates of the TABLE A thatfollows. The points for the coordinate values shown in TABLE A arerelative to the engine centerline and for a cold, i.e., room temperaturevane at various cross-sections of the vane's airfoil along its length.The positive X, Y and Z directions are axial toward the exhaust end ofthe turbine, tangential in the direction of engine rotation and radiallyoutwardly toward the static case, respectively. The X, Y, and Zcoordinates are given in distance dimensions, e.g., units of inches, andare joined smoothly at each Z location to form a smooth continuousairfoil cross-section. Each defined airfoil section in the X, Y plane isjoined smoothly with adjacent airfoil sections in the Z direction toform the complete airfoil shape.

It will be appreciated that an airfoil heats up during use, as known bya person of ordinary skill in the art. The airfoil profile will thuschange as a result of mechanical loading and temperature. Accordingly,the cold or room temperature profile, for manufacturing purposes, isgiven by X, Y and Z coordinates. A distance of plus or minus about 0.160inches (+/−0.160″) from the nominal profile in a direction normal to anysurface location along the nominal profile and which includes anycoating, defines a profile envelope for this vane airfoil, because amanufactured vane airfoil profile may be different from the nominalairfoil profile given by the following tables. The airfoil shape isrobust to this variation, without impairment of the mechanical andaerodynamic functions of the vane.

The airfoil, as embodied by the invention, can be scaled up or scaleddown geometrically for introduction into similar turbine designs.Consequently, the X, Y and Z coordinates of the nominal airfoil profilemay be a function of a constant. That is, the X, Y and Z coordinatevalues may be multiplied or divided by the same constant or number toprovide a “scaled-up” or “scaled-down” version of the vane airfoilprofile, while retaining the airfoil section shape, as embodied by theinvention.

Referring now to FIG. 1, there is illustrated a portion of a compressor,generally designated 10, having multiple stages including a first stage,generally designated 12. Each stage includes a plurality ofcircumferentially spaced stator blades, as well as rotor blades 14mounted on the compressor rotor 16. The first stage compressor statorblades 12 are circumferentially spaced one from the other, havingairfoils 18 of a particular airfoil shape or profile specified below.Referring to FIG. 2, the airfoil shape or profile includes leading andtrailing edges 20 and 22, respectively.

Referring now to FIGS. 2-7, each of the airfoils blades has an airfoilprofile defined by a Cartesian coordinate system for X, Y and Z values.The coordinate values are set forth in inches in Table I below. TheCartesian coordinate system includes orthogonally related X, Y and Zaxes with the Z axis extending along a radius from the centerline of thecompressor rotor, i.e., normal to a plane containing the X and Y values.The Z distance commences at zero in the X, Y plane at the radiallyoutermost aerodynamic section. The X axis lies parallel to thecompressor rotor centerline, i.e., the rotary axis. By defining X and Ycoordinate values at selected locations in a Z direction normal to theX, Y plane, the profile of airfoil 20 can be ascertained. By connectingthe X and Y values with smooth continuing arcs, each profile section ateach distance Z is fixed. The surface profiles at the various surfacelocations between the distances Z are connected smoothly to one anotherto form the airfoil. The tabular values given in Table I below are ininches and represent airfoil profiles at ambient, non-operating ornon-hot conditions and are for an uncoated airfoil. The sign conventionassigns a positive value Z in a radially inward direction and positiveand negative values for the X and Y coordinate values as typically usedin Cartesian coordinate systems.

To define the airfoil shape of the vane airfoil, a unique set or loci ofpoints in space are provided. This unique set or loci of points meet thestage requirements so the stage can be manufactured. This unique loci ofpoints also meets the desired requirements for stage efficiency andreduced thermal and mechanical stresses. The loci of points are arrivedat by iteration between aerodynamic and mechanical loadings enabling thecompressor to run in an efficient, safe and smooth manner.

The loci, as embodied by the invention, defines the vane airfoil profileand can comprise a set of points relative to the axis of rotation of theengine. For example, a set of points can be provided to define a vaneairfoil profile. Furthermore, the vane airfoil profile, as embodied bythe invention, can comprise a vanes for a Stage 1 rotor vane of acompressor.

A Cartesian coordinate system of X, Y and Z values given in TABLE Abelow defines a profile of a vane airfoil at various locations along itslength. The coordinate values for the X, Y and Z coordinates are setforth in inches, although other units of dimensions may be used when thevalues are appropriately converted. These values exclude fillet regionsof the platform. The Cartesian coordinate system hasorthogonally-related X, Y and Z axes. The X axis lies parallel to thecompressor rotor centerline, such as the rotary axis. A positive Xcoordinate value is axial toward the aft, for example the exhaust end ofthe compressor. A positive Y coordinate value directed aft extendstangentially in the direction of rotation of the rotor. A positive Zcoordinate value is directed radially outward toward the static casingof the compressor.

TABLE A values are generated and shown to three decimal places fordetermining the profile of the airfoil. There are typical manufacturingtolerances as well as coatings, which should be accounted for in theactual profile of the airfoil. Accordingly, the values for the profilegiven are for a nominal airfoil. It will therefore be appreciated that+/−typical manufacturing tolerances, such as, +/−values, including anycoating thicknesses, are additive to the X and Y values. Therefore, adistance of about +/−0.160 inches in a direction normal to any surfacelocation along the airfoil profile defines an airfoil profile envelopefor a vane airfoil design and compressor. In other words, a distance ofabout +/−0.160 inches in a direction normal to any surface locationalong the airfoil profile defines a range of variation between measuredpoints on the actual airfoil surface at nominal cold or room temperatureand the ideal position of those points, at the same temperature, asembodied by the invention. The vane airfoil design, as embodied by theinvention, is robust to this range of variation without impairment ofmechanical and aerodynamic functions.

The coordinate values given in the TABLE A below provide the nominalprofile envelope for an exemplary S1 stage rotor.

TABLE A X Y Z −5.8911 3.5745 −2.2710 −5.8890 3.5761 −2.2710 −5.88483.5788 −2.2710 −5.8754 3.5828 −2.2710 −5.8553 3.5852 −2.2710 −5.82413.5805 −2.2710 −5.7709 3.5612 −2.2710 −5.7041 3.5267 −2.2710 −5.61873.4738 −2.2710 −5.5155 3.4026 −2.2710 −5.3844 3.3060 −2.2710 −5.23483.1919 −2.2710 −5.0758 3.0696 −2.2710 −4.8968 2.9322 −2.2710 −4.69742.7801 −2.2710 −4.4777 2.6134 −2.2710 −4.2475 2.4397 −2.2710 −4.00682.2591 −2.2710 −3.7546 2.0729 −2.2710 −3.4899 1.8826 −2.2710 −3.21181.6894 −2.2710 −2.9198 1.4946 −2.2710 −2.6124 1.3004 −2.2710 −2.28841.1092 −2.2710 −1.9583 0.9294 −2.2710 −1.6218 0.7614 −2.2710 −1.28000.6066 −2.2710 −0.9342 0.4655 −2.2710 −0.5849 0.3369 −2.2710 −0.23240.2197 −2.2710 0.1235 0.1139 −2.2710 0.4825 0.0195 −2.2710 0.8448−0.0640 −2.2710 1.2100 −0.1369 −2.2710 1.5781 −0.1998 −2.2710 1.9366−0.2513 −2.2710 2.2841 −0.2926 −2.2710 2.6197 −0.3240 −2.2710 2.9435−0.3459 −2.2710 3.2553 −0.3595 −2.2710 3.5551 −0.3667 −2.2710 3.8426−0.3683 −2.2710 4.1051 −0.3653 −2.2710 4.3425 −0.3585 −2.2710 4.5548−0.3483 −2.2710 4.7420 −0.3358 −2.2710 4.9041 −0.3229 −2.2710 5.0411−0.3109 −2.2710 5.1582 −0.2997 −2.2710 5.2564 −0.2893 −2.2710 5.3373−0.2825 −2.2710 5.4004 −0.2954 −2.2710 5.4433 −0.3200 −2.2710 5.4697−0.3462 −2.2710 5.4867 −0.3724 −2.2710 5.4963 −0.3952 −2.2710 5.5011−0.4133 −2.2710 5.5039 −0.4337 −2.2710 5.5036 −0.4610 −2.2710 5.4971−0.4946 −2.2710 5.4810 −0.5324 −2.2710 5.4479 −0.5757 −2.2710 5.3895−0.6161 −2.2710 5.3058 −0.6479 −2.2710 5.2034 −0.6847 −2.2710 5.0812−0.7274 −2.2710 4.9378 −0.7764 −2.2710 4.7680 −0.8332 −2.2710 4.5714−0.8967 −2.2710 4.3476 −0.9654 −2.2710 4.0960 −1.0377 −2.2710 3.8169−1.1103 −2.2710 3.5102 −1.1801 −2.2710 3.1890 −1.2419 −2.2710 2.8533−1.2951 −2.2710 2.5029 −1.3390 −2.2710 2.1378 −1.3716 −2.2710 1.7576−1.3902 −2.2710 1.3620 −1.3922 −2.2710 0.9508 −1.3748 −2.2710 0.5391−1.3371 −2.2710 0.1323 −1.2784 −2.2710 −0.2690 −1.1985 −2.2710 −0.6647−1.0970 −2.2710 −1.0547 −0.9733 −2.2710 −1.4391 −0.8278 −2.2710 −1.8176−0.6612 −2.2710 −2.1856 −0.4760 −2.2710 −2.5415 −0.2726 −2.2710 −2.8851−0.0507 −2.2710 −3.2165 0.1894 −2.2710 −3.5262 0.4375 −2.2710 −3.81570.6914 −2.2710 −4.0857 0.9478 −2.2710 −4.3381 1.2022 −2.2710 −4.57281.4546 −2.2710 −4.7903 1.7044 −2.2710 −4.9934 1.9482 −2.2710 −5.17932.1883 −2.2710 −5.3429 2.4107 −2.2710 −5.4852 2.6144 −2.2710 −5.60612.7992 −2.2710 −5.7130 2.9766 −2.2710 −5.7980 3.1346 −2.2710 −5.85593.2600 −2.2710 −5.8942 3.3636 −2.2710 −5.9141 3.4439 −2.2710 −5.91853.5057 −2.2710 −5.9128 3.5398 −2.2710 −5.9037 3.5598 −2.2710 −5.89713.5687 −2.2710 −5.8932 3.5727 −2.2710 −5.7915 3.5984 −1.5610 −5.78953.5999 −1.5610 −5.7853 3.6026 −1.5610 −5.7760 3.6063 −1.5610 −5.75613.6080 −1.5610 −5.7256 3.6026 −1.5610 −5.6738 3.5824 −1.5610 −5.60873.5472 −1.5610 −5.5255 3.4939 −1.5610 −5.4250 3.4226 −1.5610 −5.29703.3262 −1.5610 −5.1508 3.2128 −1.5610 −4.9951 3.0917 −1.5610 −4.81952.9558 −1.5610 −4.6239 2.8056 −1.5610 −4.4081 2.6413 −1.5610 −4.18202.4700 −1.5610 −3.9457 2.2918 −1.5610 −3.6983 2.1079 −1.5610 −3.43871.9197 −1.5610 −3.1661 1.7286 −1.5610 −2.8800 1.5353 −1.5610 −2.57921.3418 −1.5610 −2.2625 1.1504 −1.5610 −1.9401 0.9692 −1.5610 −1.61200.7989 −1.5610 −1.2779 0.6402 −1.5610 −0.9386 0.4937 −1.5610 −0.59510.3587 −1.5610 −0.2480 0.2344 −1.5610 0.1030 0.1206 −1.5610 0.45780.0178 −1.5610 0.8157 −0.0744 −1.5610 1.1749 −0.1561 −1.5610 1.5352−0.2279 −1.5610 1.8846 −0.2886 −1.5610 2.2229 −0.3392 −1.5610 2.5501−0.3803 −1.5610 2.8660 −0.4120 −1.5610 3.1707 −0.4353 −1.5610 3.4638−0.4521 −1.5610 3.7453 −0.4635 −1.5610 4.0028 −0.4698 −1.5610 4.2363−0.4717 −1.5610 4.4456 −0.4696 −1.5610 4.6304 −0.4644 −1.5610 4.7905−0.4577 −1.5610 4.9259 −0.4509 −1.5610 5.0416 −0.4443 −1.5610 5.1388−0.4378 −1.5610 5.2188 −0.4337 −1.5610 5.2804 −0.4482 −1.5610 5.3216−0.4740 −1.5610 5.3464 −0.5008 −1.5610 5.3619 −0.5271 −1.5610 5.3703−0.5499 −1.5610 5.3743 −0.5678 −1.5610 5.3762 −0.5879 −1.5610 5.3749−0.6146 −1.5610 5.3673 −0.6474 −1.5610 5.3502 −0.6839 −1.5610 5.3160−0.7252 −1.5610 5.2571 −0.7624 −1.5610 5.1737 −0.7906 −1.5610 5.0718−0.8233 −1.5610 4.9503 −0.8611 −1.5610 4.8077 −0.9045 −1.5610 4.6390−0.9546 −1.5610 4.4438 −1.0105 −1.5610 4.2216 −1.0707 −1.5610 3.9720−1.1335 −1.5610 3.6955 −1.1958 −1.5610 3.3919 −1.2544 −1.5610 3.0743−1.3048 −1.5610 2.7427 −1.3463 −1.5610 2.3971 −1.3785 −1.5610 2.0373−1.3991 −1.5610 1.6631 −1.4055 −1.5610 1.2744 −1.3953 −1.5610 0.8709−1.3661 −1.5610 0.4674 −1.3171 −1.5610 0.0692 −1.2483 −1.5610 −0.3231−1.1594 −1.5610 −0.7095 −1.0500 −1.5610 −1.0897 −0.9196 −1.5610 −1.4641−0.7688 −1.5610 −1.8326 −0.5982 −1.5610 −2.1915 −0.4096 −1.5610 −2.5381−0.2037 −1.5610 −2.8722 0.0198 −1.5610 −3.1940 0.2605 −1.5610 −3.49440.5082 −1.5610 −3.7750 0.7606 −1.5610 −4.0372 1.0152 −1.5610 −4.28241.2667 −1.5610 −4.5100 1.5152 −1.5610 −4.7206 1.7601 −1.5610 −4.91731.9989 −1.5610 −5.0974 2.2338 −1.5610 −5.2558 2.4515 −1.5610 −5.39382.6512 −1.5610 −5.5115 2.8327 −1.5610 −5.6159 3.0076 −1.5610 −5.69933.1639 −1.5610 −5.7562 3.2878 −1.5610 −5.7939 3.3901 −1.5610 −5.81373.4694 −1.5610 −5.8184 3.5304 −1.5610 −5.8130 3.5640 −1.5610 −5.80413.5840 −1.5610 −5.7975 3.5927 −1.5610 −5.7936 3.5966 −1.5610 −5.69353.6212 −0.8520 −5.6915 3.6227 −0.8520 −5.6874 3.6252 −0.8520 −5.67823.6288 −0.8520 −5.6587 3.6303 −0.8520 −5.6287 3.6246 −0.8520 −5.57803.6043 −0.8520 −5.5143 3.5691 −0.8520 −5.4331 3.5161 −0.8520 −5.33483.4452 −0.8520 −5.2098 3.3495 −0.8520 −5.0670 3.2371 −0.8520 −4.91483.1170 −0.8520 −4.7432 2.9823 −0.8520 −4.5520 2.8334 −0.8520 −4.34102.6706 −0.8520 −4.1196 2.5012 −0.8520 −3.8881 2.3253 −0.8520 −3.64562.1437 −0.8520 −3.3913 1.9577 −0.8520 −3.1245 1.7683 −0.8520 −2.84461.5765 −0.8520 −2.5507 1.3839 −0.8520 −2.2416 1.1929 −0.8520 −1.92691.0109 −0.8520 −1.6068 0.8388 −0.8520 −1.2814 0.6773 −0.8520 −0.95060.5265 −0.8520 −0.6157 0.3865 −0.8520 −0.2773 0.2561 −0.8520 0.06460.1354 −0.8520 0.4101 0.0251 −0.8520 0.7591 −0.0755 −0.8520 1.1108−0.1665 −0.8520 1.4643 −0.2483 −0.8520 1.8076 −0.3191 −0.8520 2.1404−0.3801 −0.8520 2.4626 −0.4317 −0.8520 2.7744 −0.4741 −0.8520 3.0754−0.5079 −0.8520 3.3650 −0.5348 −0.8520 3.6429 −0.5562 −0.8520 3.8970−0.5721 −0.8520 4.1269 −0.5829 −0.8520 4.3328 −0.5892 −0.8520 4.5146−0.5915 −0.8520 4.6722 −0.5914 −0.8520 4.8056 −0.5901 −0.8520 4.9195−0.5883 −0.8520 5.0153 −0.5858 −0.8520 5.0940 −0.5841 −0.8520 5.1557−0.5985 −0.8520 5.1973 −0.6252 −0.8520 5.2218 −0.6529 −0.8520 5.2366−0.6801 −0.8520 5.2444 −0.7036 −0.8520 5.2477 −0.7221 −0.8520 5.2487−0.7418 −0.8520 5.2464 −0.7680 −0.8520 5.2377 −0.7999 −0.8520 5.2196−0.8350 −0.8520 5.1845 −0.8743 −0.8520 5.1251 −0.9082 −0.8520 5.0421−0.9326 −0.8520 4.9410 −0.9610 −0.8520 4.8203 −0.9937 −0.8520 4.6789−1.0312 −0.8520 4.5116 −1.0745 −0.8520 4.3180 −1.1224 −0.8520 4.0978−1.1738 −0.8520 3.8508 −1.2270 −0.8520 3.5773 −1.2787 −0.8520 3.2774−1.3260 −0.8520 2.9640 −1.3648 −0.8520 2.6372 −1.3948 −0.8520 2.2970−1.4152 −0.8520 1.9432 −1.4239 −0.8520 1.5758 −1.4185 −0.8520 1.1946−1.3965 −0.8520 0.7997 −1.3559 −0.8520 0.4050 −1.2965 −0.8520 0.0158−1.2183 −0.8520 −0.3672 −1.1210 −0.8520 −0.7439 −1.0046 −0.8520 −1.1142−0.8685 −0.8520 −1.4783 −0.7132 −0.8520 −1.8363 −0.5394 −0.8520 −2.1860−0.3479 −0.8520 −2.5235 −0.1401 −0.8520 −2.8484 0.0842 −0.8520 −3.16120.3245 −0.8520 −3.4530 0.5707 −0.8520 −3.7254 0.8206 −0.8520 −3.98011.0721 −0.8520 −4.2191 1.3214 −0.8520 −4.4412 1.5682 −0.8520 −4.64711.8115 −0.8520 −4.8395 2.0488 −0.8520 −5.0159 2.2818 −0.8520 −5.17112.4974 −0.8520 −5.3061 2.6947 −0.8520 −5.4210 2.8736 −0.8520 −5.52253.0450 −0.8520 −5.6034 3.1976 −0.8520 −5.6586 3.3184 −0.8520 −5.69533.4182 −0.8520 −5.7146 3.4955 −0.8520 −5.7194 3.5548 −0.8520 −5.71433.5877 −0.8520 −5.7057 3.6070 −0.8520 −5.6993 3.6156 −0.8520 −5.69563.6194 −0.8520 −5.5784 3.6516 0.0000 −5.5764 3.6531 0.0000 −5.57233.6556 0.0000 −5.5633 3.6590 0.0000 −5.5441 3.6602 0.0000 −5.5147 3.65410.0000 −5.4652 3.6335 0.0000 −5.4030 3.5982 0.0000 −5.3237 3.5452 0.0000−5.2279 3.4745 0.0000 −5.1060 3.3792 0.0000 −4.9667 3.2673 0.0000−4.8182 3.1479 0.0000 −4.6507 3.0141 0.0000 −4.4640 2.8661 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2.7950−5.1908 3.8141 2.7950 −5.1445 3.7919 2.7950 −5.0866 3.7553 2.7950−5.0133 3.7015 2.7950 −4.9247 3.6301 2.7950 −4.8122 3.5340 2.7950−4.6837 3.4216 2.7950 −4.5463 3.3020 2.7950 −4.3910 3.1683 2.7950−4.2175 3.0208 2.7950 −4.0259 2.8595 2.7950 −3.8243 2.6923 2.7950−3.6131 2.5189 2.7950 −3.3921 2.3397 2.7950 −3.1610 2.1550 2.7950−2.9194 1.9653 2.7950 −2.6668 1.7716 2.7950 −2.4020 1.5752 2.7950−2.1242 1.3776 2.7950 −1.8419 1.1860 2.7950 −1.5547 1.0012 2.7950−1.2622 0.8237 2.7950 −0.9652 0.6536 2.7950 −0.6646 0.4902 2.7950−0.3606 0.3332 2.7950 −0.0532 0.1827 2.7950 0.2570 0.0379 2.7950 0.5695−0.1017 2.7950 0.8844 −0.2358 2.7950 1.2015 −0.3645 2.7950 1.5102−0.4839 2.7950 1.8099 −0.5944 2.7950 2.1005 −0.6966 2.7950 2.3816−0.7910 2.7950 2.6532 −0.8781 2.7950 2.9150 −0.9582 2.7950 3.1669−1.0321 2.7950 3.3976 −1.0972 2.7950 3.6068 −1.1543 2.7950 3.7944−1.2038 2.7950 3.9603 −1.2460 2.7950 4.1044 −1.2813 2.7950 4.2266−1.3104 2.7950 4.3311 −1.3348 2.7950 4.4189 −1.3550 2.7950 4.4913−1.3715 2.7950 4.5455 −1.3955 2.7950 4.5780 −1.4288 2.7950 4.5942−1.4597 2.7950 4.6015 −1.4880 2.7950 4.6032 −1.5113 2.7950 4.6021−1.5289 2.7950 4.5987 −1.5469 2.7950 4.5911 −1.5698 2.7950 4.5766−1.5966 2.7950 4.5529 −1.6243 2.7950 4.5129 −1.6516 2.7950 4.4518−1.6666 2.7950 4.3725 −1.6712 2.7950 4.2761 −1.6762 2.7950 4.1613−1.6815 2.7950 4.0270 −1.6869 2.7950 3.8682 −1.6919 2.7950 3.6850−1.6955 2.7950 3.4773 −1.6968 2.7950 3.2451 −1.6944 2.7950 2.9889−1.6861 2.7950 2.7089 −1.6703 2.7950 2.4174 −1.6462 2.7950 2.1145−1.6128 2.7950 1.8003 −1.5687 2.7950 1.4754 −1.5127 2.7950 1.1419−1.4436 2.7950 0.8008 −1.3602 2.7950 0.4525 −1.2610 2.7950 0.1089−1.1485 2.7950 −0.2298 −1.0225 2.7950 −0.5633 −0.8816 2.7950 −0.8915−0.7261 2.7950 −1.2146 −0.5563 2.7950 −1.5319 −0.3721 2.7950 −1.8400−0.1759 2.7950 −2.1390 0.0314 2.7950 −2.4289 0.2497 2.7950 −2.70950.4793 2.7950 −2.9809 0.7200 2.7950 −3.2351 0.9625 2.7950 −3.4733 1.20562.7950 −3.6970 1.4472 2.7950 −3.9074 1.6851 2.7950 −4.1035 1.9189 2.7950−4.2870 2.1475 2.7950 −4.4592 2.3695 2.7950 −4.6191 2.5853 2.7950−4.7608 2.7843 2.7950 −4.8849 2.9657 2.7950 −4.9910 3.1298 2.7950−5.0853 3.2869 2.7950 −5.1607 3.4267 2.7950 −5.2126 3.5373 2.7950−5.2476 3.6286 2.7950 −5.2669 3.6993 2.7950 −5.2731 3.7538 2.7950−5.2697 3.7841 2.7950 −5.2625 3.8023 2.7950 −5.2569 3.8103 2.7950−5.2534 3.8138 2.7950 −5.1866 3.8611 3.4040 −5.1847 3.8625 3.4040−5.1807 3.8647 3.4040 −5.1719 3.8674 3.4040 −5.1536 3.8669 3.4040−5.1263 3.8588 3.4040 −5.0806 3.8360 3.4040 −5.0234 3.7990 3.4040−4.9510 3.7446 3.4040 −4.8637 3.6727 3.4040 −4.7528 3.5760 3.4040−4.6259 3.4629 3.4040 −4.4903 3.3427 3.4040 −4.3370 3.2083 3.4040−4.1657 3.0601 3.4040 −3.9765 2.8980 3.4040 −3.7776 2.7298 3.4040−3.5692 2.5552 3.4040 −3.3513 2.3744 3.4040 −3.1236 2.1878 3.4040−2.8858 1.9959 3.4040 −2.6372 1.7994 3.4040 −2.3768 1.5997 3.4040−2.1036 1.3983 3.4040 −1.8260 1.2026 3.4040 −1.5435 1.0133 3.4040−1.2558 0.8313 3.4040 −0.9636 0.6569 3.4040 −0.6677 0.4890 3.4040−0.3685 0.3269 3.4040 −0.0660 0.1707 3.4040 0.2391 0.0198 3.4040 0.5464−0.1265 3.4040 0.8560 −0.2678 3.4040 1.1680 −0.4041 3.4040 1.4715−0.5312 3.4040 1.7661 −0.6498 3.4040 2.0517 −0.7604 3.4040 2.3280−0.8636 3.4040 2.5947 −0.9599 3.4040 2.8519 −1.0497 3.4040 3.0991−1.1332 3.4040 3.3256 −1.2074 3.4040 3.5311 −1.2727 3.4040 3.7154−1.3298 3.4040 3.8783 −1.3790 3.4040 4.0199 −1.4204 3.4040 4.1399−1.4548 3.4040 4.2426 −1.4838 3.4040 4.3290 −1.5079 3.4040 4.4001−1.5275 3.4040 4.4533 −1.5527 3.4040 4.4841 −1.5862 3.4040 4.4990−1.6172 3.4040 4.5051 −1.6450 3.4040 4.5060 −1.6680 3.4040 4.5042−1.6851 3.4040 4.5002 −1.7028 3.4040 4.4916 −1.7251 3.4040 4.4760−1.7509 3.4040 4.4511 −1.7769 3.4040 4.4097 −1.8011 3.4040 4.3483−1.8111 3.4040 4.2697 −1.8119 3.4040 4.1742 −1.8122 3.4040 4.0605−1.8118 3.4040 3.9276 −1.8104 3.4040 3.7705 −1.8073 3.4040 3.5893−1.8012 3.4040 3.3840 −1.7915 3.4040 3.1548 −1.7769 3.4040 2.9021−1.7559 3.4040 2.6260 −1.7270 3.4040 2.3388 −1.6900 3.4040 2.0406−1.6439 3.4040 1.7316 −1.5874 3.4040 1.4129 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−4.7168 3.6022 3.7590−4.5910 3.4886 3.7590 −4.4564 3.3679 3.7590 −4.3041 3.2330 3.7590−4.1341 3.0842 3.7590 −3.9462 2.9214 3.7590 −3.7489 2.7523 3.7590−3.5422 2.5767 3.7590 −3.3261 2.3948 3.7590 −3.1005 2.2068 3.7590−2.8648 2.0132 3.7590 −2.6187 1.8148 3.7590 −2.3610 1.6128 3.7590−2.0907 1.4086 3.7590 −1.8162 1.2097 3.7590 −1.5367 1.0172 3.7590−1.2520 0.8323 3.7590 −0.9627 0.6551 3.7590 −0.6695 0.4844 3.7590−0.3729 0.3194 3.7590 −0.0732 0.1600 3.7590 0.2287 0.0057 3.7590 0.5328−0.1442 3.7590 0.8392 −0.2892 3.7590 1.1478 −0.4293 3.7590 1.4481−0.5605 3.7590 1.7399 −0.6833 3.7590 2.0229 −0.7983 3.7590 2.2966−0.9060 3.7590 2.5608 −1.0069 3.7590 2.8153 −1.1014 3.7590 3.0601−1.1898 3.7590 3.2843 −1.2685 3.7590 3.4876 −1.3382 3.7590 3.6701−1.3992 3.7590 3.8314 −1.4520 3.7590 3.9715 −1.4969 3.7590 4.0902−1.5342 3.7590 4.1918 −1.5657 3.7590 4.2772 −1.5920 3.7590 4.3476−1.6134 3.7590 4.4011 −1.6379 3.7590 4.4325 −1.6715 3.7590 4.4474−1.7026 3.7590 4.4535 −1.7308 3.7590 4.4540 −1.7540 3.7590 4.4518−1.7713 3.7590 4.4475 −1.7886 3.7590 4.4384 −1.8106 3.7590 4.4221−1.8356 3.7590 4.3964 −1.8605 3.7590 4.3542 −1.8825 3.7590 4.2928−1.8890 3.7590 4.2148 −1.8874 3.7590 4.1201 −1.8849 3.7590 4.0074−1.8811 3.7590 3.8755 −1.8757 3.7590 3.7198 −1.8678 3.7590 3.5403−1.8564 3.7590 3.3369 −1.8407 3.7590 3.1102 −1.8199 3.7590 2.8605−1.7924 3.7590 2.5881 −1.7570 3.7590 2.3053 −1.7140 3.7590 2.0121−1.6621 3.7590 1.7090 −1.6003 3.7590 1.3960 −1.5274 3.7590 1.0736−1.4422 3.7590 0.7420 −1.3431 3.7590 0.4016 −1.2283 3.7590 0.0646−1.1009 3.7590 −0.2657 −0.9614 3.7590 −0.5886 −0.8094 3.7590 −0.9044−0.6453 3.7590 −1.2133 −0.4695 3.7590 −1.5153 −0.2819 3.7590 −1.8104−0.0826 3.7590 −2.0984 0.1287 3.7590 −2.3794 0.3520 3.7590 −2.65250.5872 3.7590 −2.9164 0.8321 3.7590 −3.1635 1.0770 3.7590 −3.3950 1.32063.7590 −3.6127 1.5612 3.7590 −3.8176 1.7970 3.7590 −4.0095 2.0280 3.7590−4.1896 2.2532 3.7590 −4.3591 2.4715 3.7590 −4.5171 2.6835 3.7590−4.6574 2.8786 3.7590 −4.7806 3.0564 3.7590 −4.8861 3.2171 3.7590−4.9799 3.3711 3.7590 −5.0551 3.5081 3.7590 −5.1068 3.6167 3.7590−5.1419 3.7062 3.7590 −5.1614 3.7756 3.7590 −5.1681 3.8292 3.7590−5.1652 3.8591 3.7590 −5.1584 3.8770 3.7590 −5.1529 3.8849 3.7590−5.1495 3.8884 3.7590 −5.1057 3.9213 4.1140 −5.1038 3.9226 4.1140−5.0998 3.9248 4.1140 −5.0910 3.9272 4.1140 −5.0728 3.9262 4.1140−5.0458 3.9177 4.1140 −5.0007 3.8941 4.1140 −4.9445 3.8564 4.1140−4.8733 3.8013 4.1140 −4.7874 3.7285 4.1140 −4.6783 3.6308 4.1140−4.5535 3.5167 4.1140 −4.4200 3.3955 4.1140 −4.2689 3.2601 4.1140−4.1002 3.1106 4.1140 −3.9138 2.9470 4.1140 −3.7181 2.7770 4.1140−3.5133 2.6003 4.1140 −3.2993 2.4171 4.1140 −3.0758 2.2276 4.1140−2.8426 2.0323 4.1140 −2.5991 1.8318 4.1140 −2.3444 1.6271 4.1140−2.0775 1.4198 4.1140 −1.8065 1.2174 4.1140 −1.5306 1.0212 4.1140−1.2494 0.8328 4.1140 −0.9631 0.6520 4.1140 −0.6728 0.4781 4.1140−0.3792 0.3099 4.1140 −0.0825 0.1471 4.1140 0.2168 −0.0111 4.1140 0.5182−0.1649 4.1140 0.8221 −0.3140 4.1140 1.1281 −0.4584 4.1140 1.4261−0.5938 4.1140 1.7153 −0.7208 4.1140 1.9957 −0.8398 4.1140 2.2669−0.9514 4.1140 2.5286 −1.0564 4.1140 2.7809 −1.1549 4.1140 3.0234−1.2472 4.1140 3.2456 −1.3295 4.1140 3.4472 −1.4024 4.1140 3.6280−1.4665 4.1140 3.7879 −1.5222 4.1140 3.9267 −1.5696 4.1140 4.0443−1.6092 4.1140 4.1450 −1.6427 4.1140 4.2296 −1.6707 4.1140 4.2993−1.6936 4.1140 4.3528 −1.7177 4.1140 4.3843 −1.7509 4.1140 4.3991−1.7820 4.1140 4.4050 −1.8101 4.1140 4.4052 −1.8332 4.1140 4.4027−1.8504 4.1140 4.3980 −1.8676 4.1140 4.3884 −1.8892 4.1140 4.3714−1.9135 4.1140 4.3448 −1.9371 4.1140 4.3019 −1.9567 4.1140 4.2404−1.9599 4.1140 4.1630 −1.9563 4.1140 4.0689 −1.9512 4.1140 3.9570−1.9445 4.1140 3.8261 −1.9358 4.1140 3.6715 −1.9240 4.1140 3.4934−1.9082 4.1140 3.2916 −1.8876 4.1140 3.0668 −1.8615 4.1140 2.8192−1.8287 4.1140 2.5491 −1.7877 4.1140 2.2687 −1.7390 4.1140 1.9780−1.6814 4.1140 1.6775 −1.6139 4.1140 1.3674 −1.5354 4.1140 1.0479−1.4447 4.1140 0.7193 −1.3401 4.1140 0.3821 −1.2200 4.1140 0.0499−1.0881 4.1140 −0.2757 −0.9446 4.1140 −0.5943 −0.7888 4.1140 −0.9061−0.6211 4.1140 −1.2114 −0.4419 4.1140 −1.5101 −0.2514 4.1140 −1.8021−0.0489 4.1140 −2.0871 0.1657 4.1140 −2.3648 0.3922 4.1140 −2.63320.6289 4.1140 −2.8928 0.8750 4.1140 −3.1363 1.1207 4.1140 −3.3650 1.36464.1140 −3.5801 1.6049 4.1140 −3.7829 1.8401 4.1140 −3.9730 2.0704 4.1140−4.1517 2.2946 4.1140 −4.3200 2.5119 4.1140 −4.4772 2.7227 4.1140−4.6169 2.9165 4.1140 −4.7396 3.0932 4.1140 −4.8448 3.2528 4.1140−4.9383 3.4058 4.1140 −5.0131 3.5419 4.1140 −5.0647 3.6497 4.1140−5.0996 3.7387 4.1140 −5.1191 3.8077 4.1140 −5.1259 3.8609 4.1140−5.1231 3.8906 4.1140 −5.1164 3.9084 4.1140 −5.1110 3.9163 4.1140−5.1076 3.9197 4.1140 −5.0108 3.9925 4.8230 −5.0089 3.9938 4.8230−5.0049 3.9960 4.8230 −4.9961 3.9981 4.8230 −4.9780 3.9967 4.8230−4.9513 3.9875 4.8230 −4.9068 3.9632 4.8230 −4.8514 3.9247 4.8230−4.7814 3.8687 4.8230 −4.6969 3.7949 4.8230 −4.5895 3.6960 4.8230−4.4667 3.5807 4.8230 −4.3351 3.4584 4.8230 −4.1861 3.3218 4.8230−4.0198 3.1709 4.8230 −3.8362 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2.8520−1.5199 5.5320 3.0659 −1.6166 5.5320 3.2602 −1.7022 5.5320 3.4347−1.7774 5.5320 3.5891 −1.8428 5.5320 3.7232 −1.8986 5.5320 3.8369−1.9453 5.5320 3.9342 −1.9850 5.5320 4.0160 −2.0182 5.5320 4.0834−2.0454 5.5320 4.1370 −2.0677 5.5320 4.1716 −2.0965 5.5320 4.1879−2.1266 5.5320 4.1938 −2.1545 5.5320 4.1932 −2.1774 5.5320 4.1897−2.1943 5.5320 4.1836 −2.2107 5.5320 4.1719 −2.2307 5.5320 4.1520−2.2518 5.5320 4.1222 −2.2697 5.5320 4.0767 −2.2779 5.5320 4.0163−2.2707 5.5320 3.9409 −2.2605 5.5320 3.8494 −2.2476 5.5320 3.7405−2.2315 5.5320 3.6133 −2.2118 5.5320 3.4633 −2.1870 5.5320 3.2904−2.1562 5.5320 3.0952 −2.1187 5.5320 2.8779 −2.0735 5.5320 2.6389−2.0195 5.5320 2.3785 −1.9552 5.5320 2.1086 −1.8823 5.5320 1.8292−1.7996 5.5320 1.5408 −1.7062 5.5320 1.2435 −1.6013 5.5320 0.9378−1.4836 5.5320 0.6255 −1.3525 5.5320 0.3083 −1.2072 5.5320 −0.0029−1.0520 5.5320 −0.3078 −0.8864 5.5320 −0.6061 −0.7099 5.5320 −0.8978−0.5226 5.5320 −1.1832 −0.3250 5.5320 −1.4624 −0.1171 5.5320 −1.73540.1010 5.5320 −2.0021 0.3293 5.5320 −2.2613 0.5661 5.5320 −2.5128 0.81065.5320 −2.7571 1.0622 5.5320 −2.9876 1.3113 5.5320 −3.2052 1.5565 5.5320−3.4110 1.7964 5.5320 −3.6060 2.0301 5.5320 −3.7901 2.2577 5.5320−3.9640 2.4785 5.5320 −4.1285 2.6917 5.5320 −4.2829 2.8980 5.5320−4.4206 3.0873 5.5320 −4.5421 3.2596 5.5320 −4.6465 3.4152 5.5320−4.7394 3.5642 5.5320 −4.8140 3.6970 5.5320 −4.8654 3.8022 5.5320−4.9004 3.8890 5.5320 −4.9203 3.9564 5.5320 −4.9278 4.0084 5.5320−4.9258 4.0376 5.5320 −4.9196 4.0552 5.5320 −4.9143 4.0630 5.5320−4.9110 4.0664 5.5320 −4.8116 4.1380 6.2420 −4.8097 4.1392 6.2420−4.8056 4.1412 6.2420 −4.7967 4.1428 6.2420 −4.7789 4.1403 6.2420−4.7530 4.1300 6.2420 −4.7098 4.1042 6.2420 −4.6562 4.0643 6.2420−4.5884 4.0067 6.2420 −4.5066 3.9312 6.2420 −4.4027 3.8304 6.2420−4.2836 3.7133 6.2420 −4.1556 3.5894 6.2420 −4.0106 3.4509 6.2420−3.8487 3.2980 6.2420 −3.6700 3.1303 6.2420 −3.4829 2.9553 6.2420−3.2877 2.7728 6.2420 −3.0844 2.5827 6.2420 −2.8730 2.3848 6.2420−2.6533 2.1794 6.2420 −2.4251 1.9670 6.2420 −2.1877 1.7480 6.2420−1.9407 1.5232 6.2420 −1.6916 1.3008 6.2420 −1.4398 1.0815 6.2420−1.1845 0.8663 6.2420 −0.9252 0.6557 6.2420 −0.6617 0.4499 6.2420−0.3943 0.2494 6.2420 −0.1232 0.0539 6.2420 0.1510 −0.1372 6.2420 0.4278−0.3246 6.2420 0.7073 −0.5077 6.2420 0.9894 −0.6864 6.2420 1.2646−0.8551 6.2420 1.5326 −1.0143 6.2420 1.7931 −1.1643 6.2420 2.0459−1.3058 6.2420 2.2904 −1.4393 6.2420 2.5264 −1.5649 6.2420 2.7540−1.6828 6.2420 2.9630 −1.7879 6.2420 3.1532 −1.8810 6.2420 3.3242−1.9626 6.2420 3.4756 −2.0334 6.2420 3.6073 −2.0938 6.2420 3.7190−2.1443 6.2420 3.8146 −2.1871 6.2420 3.8951 −2.2228 6.2420 3.9613−2.2521 6.2420 4.0144 −2.2755 6.2420 4.0497 −2.3017 6.2420 4.0663−2.3303 6.2420 4.0720 −2.3572 6.2420 4.0711 −2.3793 6.2420 4.0673−2.3954 6.2420 4.0606 −2.4113 6.2420 4.0478 −2.4305 6.2420 4.0265−2.4496 6.2420 3.9951 −2.4638 6.2420 3.9492 −2.4647 6.2420 3.8898−2.4544 6.2420 3.8155 −2.4411 6.2420 3.7254 −2.4243 6.2420 3.6183−2.4035 6.2420 3.4932 −2.3781 6.2420 3.3457 −2.3465 6.2420 3.1761−2.3075 6.2420 2.9848 −2.2606 6.2420 2.7721 −2.2047 6.2420 2.5383−2.1386 6.2420 2.2839 −2.0610 6.2420 2.0204 −1.9741 6.2420 1.7481−1.8768 6.2420 1.4673 −1.7682 6.2420 1.1782 −1.6477 6.2420 0.8827−1.5149 6.2420 0.5820 −1.3688 6.2420 0.2768 −1.2086 6.2420 −0.0225−1.0391 6.2420 −0.3157 −0.8601 6.2420 −0.6024 −0.6709 6.2420 −0.8827−0.4717 6.2420 −1.1570 −0.2630 6.2420 −1.4254 −0.0451 6.2420 −1.68820.1816 6.2420 −1.9452 0.4162 6.2420 −2.1957 0.6573 6.2420 −2.4398 0.90466.2420 −2.6780 1.1578 6.2420 −2.9034 1.4074 6.2420 −3.1167 1.6523 6.2420−3.3191 1.8912 6.2420 −3.5112 2.1236 6.2420 −3.6931 2.3495 6.2420−3.8654 2.5682 6.2420 −4.0287 2.7792 6.2420 −4.1822 2.9830 6.2420−4.3195 3.1700 6.2420 −4.4407 3.3401 6.2420 −4.5452 3.4935 6.2420−4.6383 3.6405 6.2420 −4.7131 3.7714 6.2420 −4.7649 3.8752 6.2420−4.8004 3.9609 6.2420 −4.8209 4.0274 6.2420 −4.8291 4.0789 6.2420−4.8276 4.1079 6.2420 −4.8218 4.1254 6.2420 −4.8167 4.1331 6.2420−4.8134 4.1365 6.2420 −4.6349 4.2490 7.6610 −4.6330 4.2502 7.6610−4.6289 4.2520 7.6610 −4.6200 4.2530 7.6610 −4.6025 4.2492 7.6610−4.5773 4.2375 7.6610 −4.5356 4.2099 7.6610 −4.4839 4.1682 7.6610−4.4185 4.1086 7.6610 −4.3398 4.0308 7.6610 −4.2395 3.9274 7.6610−4.1240 3.8080 7.6610 −3.9998 3.6816 7.6610 −3.8588 3.5405 7.6610−3.7013 3.3847 7.6610 −3.5275 3.2139 7.6610 −3.3454 3.0357 7.6610−3.1554 2.8498 7.6610 −2.9576 2.6559 7.6610 −2.7522 2.4540 7.6610−2.5390 2.2442 7.6610 −2.3177 2.0268 7.6610 −2.0884 1.8019 7.6610−1.8508 1.5695 7.6610 −1.6127 1.3376 7.6610 −1.3738 1.1065 7.6610−1.1334 0.8771 7.6610 −0.8911 0.6497 7.6610 −0.6465 0.4247 7.6610−0.3995 0.2024 7.6610 −0.1496 −0.0166 7.6610 0.1032 −0.2324 7.66100.3584 −0.4450 7.6610 0.6168 −0.6537 7.6610 0.8784 −0.8581 7.6610 1.1343−1.0520 7.6610 1.3843 −1.2354 7.6610 1.6280 −1.4089 7.6610 1.8649−1.5726 7.6610 2.0947 −1.7270 7.6610 2.3172 −1.8725 7.6610 2.5323−2.0090 7.6610 2.7306 −2.1308 7.6610 2.9114 −2.2386 7.6610 3.0745−2.3330 7.6610 3.2192 −2.4148 7.6610 3.3453 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5.6153 19.0110 −3.4950 5.6446 19.0110 −3.4955 5.6635 19.0110−3.4940 5.6728 19.0110 −3.4919 5.6770 19.0110 −3.3973 5.9211 19.4830−3.3949 5.9211 19.4830 −3.3910 5.9183 19.4830 −3.3849 5.9109 19.4830−3.3750 5.8945 19.4830 −3.3615 5.8678 19.4830 −3.3398 5.8185 19.4830−3.3129 5.7519 19.4830 −3.2781 5.6627 19.4830 −3.2341 5.5513 19.4830−3.1751 5.4073 19.4830 −3.1042 5.2423 19.4830 −3.0256 5.0678 19.4830−2.9335 4.8733 19.4830 −2.8269 4.6593 19.4830 −2.7064 4.4257 19.4830−2.5780 4.1826 19.4830 −2.4417 3.9302 19.4830 −2.2996 3.6673 19.4830−2.1526 3.3935 19.4830 −2.0013 3.1085 19.4830 −1.8461 2.8120 19.4830−1.6875 2.5039 19.4830 −1.5255 2.1841 19.4830 −1.3658 1.8630 19.4830−1.2087 1.5407 19.4830 −1.0543 1.2171 19.4830 −0.9027 0.8923 19.4830−0.7540 0.5662 19.4830 −0.6084 0.2387 19.4830 −0.4659 −0.0902 19.4830−0.3267 −0.4206 19.4830 −0.1908 −0.7524 19.4830 −0.0582 −1.0856 19.48300.0708 −1.4201 19.4830 0.1921 −1.7447 19.4830 0.3055 −2.0596 19.48300.4111 −2.3646 19.4830 0.5095 −2.6594 19.4830 0.6019 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−0.9515 0.0805 19.4830 −1.0951 0.4098 19.4830−1.2400 0.7386 19.4830 −1.3862 1.0667 19.4830 −1.5336 1.3944 19.4830−1.6819 1.7217 19.4830 −1.8308 2.0486 19.4830 −1.9802 2.3753 19.4830−2.1251 2.6910 19.4830 −2.2653 2.9956 19.4830 −2.4004 3.2894 19.4830−2.5299 3.5725 19.4830 −2.6545 3.8448 19.4830 −2.7719 4.1071 19.4830−2.8809 4.3601 19.4830 −2.9826 4.6031 19.4830 −3.0711 4.8257 19.4830−3.1467 5.0275 19.4830 −3.2113 5.2079 19.4830 −3.2690 5.3781 19.4830−3.3166 5.5264 19.4830 −3.3509 5.6411 19.4830 −3.3755 5.7338 19.4830−3.3912 5.8039 19.4830 −3.4002 5.8570 19.4830 −3.4032 5.8868 19.4830−3.4031 5.9060 19.4830 −3.4014 5.9154 19.4830 −3.3992 5.9196 19.4830−3.3049 6.1732 19.9560 −3.3025 6.1729 19.9560 −3.2987 6.1698 19.9560−3.2931 6.1618 19.9560 −3.2842 6.1446 19.9560 −3.2723 6.1166 19.9560−3.2534 6.0654 19.9560 −3.2304 5.9963 19.9560 −3.2007 5.9039 19.9560−3.1626 5.7887 19.9560 −3.1111 5.6395 19.9560 −3.0485 5.4686 19.9560−2.9788 5.2875 19.9560 −2.8962 5.0857 19.9560 −2.7995 4.8637 19.9560−2.6893 4.6211 19.9560 −2.5710 4.3689 19.9560 −2.4446 4.1070 19.9560−2.3118 3.8347 19.9560 −2.1741 3.5513 19.9560 −2.0318 3.2567 19.9560−1.8857 2.9506 19.9560 −1.7359 2.6328 19.9560 −1.5826 2.3032 19.9560−1.4313 1.9728 19.9560 −1.2825 1.6412 19.9560 −1.1361 1.3085 19.9560−0.9923 0.9747 19.9560 −0.8511 0.6396 19.9560 −0.7129 0.3033 19.9560−0.5779 −0.0343 19.9560 −0.4462 −0.3731 19.9560 −0.3177 −0.7132 19.9560−0.1924 −1.0545 19.9560 −0.0703 −1.3970 19.9560 0.0441 −1.7294 19.95600.1505 −2.0516 19.9560 0.2488 −2.3637 19.9560 0.3395 −2.6655 19.95600.4241 −2.9565 19.9560 0.5046 −3.2361 19.9560 0.5829 −3.5037 19.95600.6569 −3.7473 19.9560 0.7272 −3.9667 19.9560 0.7942 −4.1616 19.95600.8579 −4.3318 19.9560 0.9158 −4.4784 19.9560 0.9662 −4.6019 19.95601.0108 −4.7068 19.9560 1.0492 −4.7945 19.9560 1.0814 −4.8665 19.95601.1073 −4.9240 19.9560 1.1273 −4.9681 19.9560 1.1424 −5.0012 19.95601.1546 −5.0289 19.9560 1.1527 −5.0523 19.9560 1.1424 −5.0668 19.95601.1255 −5.0741 19.9560 1.1037 −5.0645 19.9560 1.0852 −5.0402 19.95601.0634 −5.0108 19.9560 1.0345 −4.9714 19.9560 0.9976 −4.9198 19.95600.9522 −4.8549 19.9560 0.8985 −4.7749 19.9560 0.8376 −4.6778 19.95600.7705 −4.5616 19.9560 0.6953 −4.4222 19.9560 0.6134 −4.2592 19.95600.5271 −4.0719 19.9560 0.4370 −3.8598 19.9560 0.3432 −3.6229 19.95600.2455 −3.3615 19.9560 0.1469 −3.0872 19.9560 0.0455 −2.8009 19.9560−0.0598 −2.5032 19.9560 −0.1702 −2.1944 19.9560 −0.2860 −1.8746 19.9560−0.4075 −1.5440 19.9560 −0.5349 −1.2027 19.9560 −0.6638 −0.8619 19.9560−0.7943 −0.5217 19.9560 −0.9266 −0.1822 19.9560 −1.0606 0.1567 19.9560−1.1961 0.4950 19.9560 −1.3327 0.8329 19.9560 −1.4706 1.1702 19.9560−1.6095 1.5072 19.9560 −1.7491 1.8438 19.9560 −1.8892 2.1802 19.9560−2.0295 2.5166 19.9560 −2.1651 2.8417 19.9560 −2.2961 3.1556 19.9560−2.4216 3.4587 19.9560 −2.5413 3.7510 19.9560 −2.6558 4.0322 19.9560−2.7626 4.3035 19.9560 −2.8610 4.5650 19.9560 −2.9520 4.8162 19.9560−3.0304 5.0462 19.9560 −3.0965 5.2547 19.9560 −3.1524 5.4409 19.9560−3.2020 5.6163 19.9560 −3.2424 5.7691 19.9560 −3.2711 5.8872 19.9560−3.2914 5.9823 19.9560 −3.3038 6.0541 19.9560 −3.3105 6.1084 19.9560−3.3121 6.1387 19.9560 −3.3113 6.1581 19.9560 −3.3092 6.1676 19.9560−3.3069 6.1718 19.9560 −3.2141 6.4298 20.4290 −3.2117 6.4290 20.4290−3.2082 6.4255 20.4290 −3.2030 6.4171 20.4290 −3.1949 6.3991 20.4290−3.1844 6.3702 20.4290 −3.1680 6.3173 20.4290 −3.1483 6.2460 20.4290−3.1231 6.1508 20.4290 −3.0907 6.0319 20.4290 −3.0465 5.8780 20.4290−2.9921 5.7015 20.4290 −2.9309 5.5144 20.4290 −2.8574 5.3057 20.4290−2.7706 5.0758 20.4290 −2.6708 4.8245 20.4290 −2.5633 4.5630 20.4290−2.4475 4.2915 20.4290 −2.3249 4.0095 20.4290 −2.1972 3.7162 20.4290−2.0647 3.4117 20.4290 −1.9281 3.0955 20.4290 −1.7876 2.7676 20.4290−1.6434 2.4279 20.4290 −1.5007 2.0875 20.4290 −1.3599 1.7464 20.4290−1.2212 1.4044 20.4290 −1.0846 1.0615 20.4290 −0.9505 0.7176 20.4290−0.8191 0.3728 20.4290 −0.6907 0.0268 20.4290 −0.5654 −0.3203 20.4290−0.4434 −0.6686 20.4290 −0.3250 −1.0182 20.4290 −0.2106 −1.3691 20.4290−0.1044 −1.7097 20.4290 −0.0066 −2.0400 20.4290 0.0831 −2.3598 20.42900.1656 −2.6689 20.4290 0.2427 −2.9668 20.4290 0.3163 −3.2528 20.42900.3884 −3.5265 20.4290 0.4569 −3.7757 20.4290 0.5226 −4.0002 20.42900.5855 −4.1996 20.4290 0.6450 −4.3743 20.4290 0.6991 −4.5249 20.42900.7461 −4.6519 20.4290 0.7875 −4.7599 20.4290 0.8233 −4.8504 20.42900.8531 −4.9246 20.4290 0.8772 −4.9839 20.4290 0.8959 −5.0295 20.42900.9099 −5.0636 20.4290 0.9212 −5.0922 20.4290 0.9186 −5.1169 20.42900.9074 −5.1321 20.4290 0.8903 −5.1397 20.4290 0.8680 −5.1303 20.42900.8500 −5.1051 20.4290 0.8287 −5.0746 20.4290 0.8006 −5.0337 20.42900.7645 −4.9802 20.4290 0.7202 −4.9129 20.4290 0.6680 −4.8301 20.42900.6088 −4.7297 20.4290 0.5439 −4.6097 20.4290 0.4717 −4.4659 20.42900.3940 −4.2979 20.4290 0.3130 −4.1047 20.4290 0.2293 −3.8861 20.42900.1427 −3.6422 20.4290 0.0526 −3.3733 20.4290 −0.0383 −3.0915 20.4290−0.1319 −2.7975 20.4290 −0.2295 −2.4918 20.4290 −0.3320 −2.1748 20.4290−0.4400 −1.8466 20.4290 −0.5539 −1.5074 20.4290 −0.6740 −1.1573 20.4290−0.7959 −0.8078 20.4290 −0.9195 −0.4589 20.4290 −1.0449 −0.1105 20.4290−1.1718 0.2373 20.4290 −1.2999 0.5846 20.4290 −1.4289 0.9317 20.4290−1.5588 1.2784 20.4290 −1.6893 1.6249 20.4290 −1.8201 1.9712 20.4290−1.9509 2.3176 20.4290 −2.0813 2.6641 20.4290 −2.2069 2.9992 20.4290−2.3275 3.3231 20.4290 −2.4424 3.6358 20.4290 −2.5513 3.9376 20.4290−2.6551 4.2282 20.4290 −2.7508 4.5085 20.4290 −2.8386 4.7784 20.4290−2.9199 5.0374 20.4290 −2.9893 5.2743 20.4290 −3.0472 5.4888 20.4290−3.0958 5.6803 20.4290 −3.1381 5.8606 20.4290 −3.1720 6.0175 20.4290−3.1954 6.1387 20.4290 −3.2113 6.2362 20.4290 −3.2204 6.3098 20.4290−3.2243 6.3652 20.4290 −3.2243 6.3960 20.4290 −3.2222 6.4157 20.4290−3.2194 6.4251 20.4290 −3.2164 6.4290 20.4290

In the exemplary embodiments, as embodied by the invention, for examplethe stage compressor vane, there are many airfoils, which are un-cooled.For reference purposes only, there is established point-0 passingthrough the intersection of the airfoil and the platform along thestacking axis.

It will also be appreciated that the exemplary airfoil(s) disclosed inthe above TABLE A may be scaled up or down geometrically for use inother similar compressor designs. Consequently, the coordinate valuesset forth in TABLE A may be scaled upwardly or downwardly such TABLE Athe airfoil profile shape remains unchanged. A scaled version of thecoordinates in the TABLE A would be represented by X, Y and Z coordinatevalues of the TABLE A multiplied or divided by a constant.

In particular, as embodied by the invention, the airfoil as defined byTABLE A, can be applied in a compressor of a turbine, for example, butnot limited to, as General Electric “7FA+e” compressor. Moreover, thevane airfoil profile, as embodied by the invention, can comprise a stage1 rotor vane of a compressor. This compressor is merely illustrative ofthe intended applications for the airfoil, as embodied by the invention.Moreover, it is envisioned that the airfoil of TABLE A, as embodied bythe invention, can also be used as rotor vanes in GE Frame F-classturbines, as well as GE's Frame 6 and 9 turbines, given the scaling ofthe airfoil, as embodied by the invention.

The airfoils impart kinetic energy to the airflow and therefore bringabout a desired flow across the compressor. The airfoils turn the fluidflow, slow the fluid flow velocity (in the respective airfoil frame ofreference), and yield a rise in the static pressure of the fluid flow.The configuration of the airfoil (along with its interaction withsurrounding airfoils), as embodied by the invention, including itsperipheral surface provides for stage airflow efficiency, enhancedaeromechanics, smooth laminar flow from stage to stage, reduced thermalstresses, enhanced interrelation of the stages to effectively pass theairflow from stage to stage, and reduced mechanical stresses, amongother desirable aspects of the invention. Typically, multiple rows ofairfoil stages, such as, but not limited to, rotor/rotor airfoils, arestacked to achieve a desired discharge to inlet pressure ratio. Airfoilscan be secured to wheels or a case by an appropriate attachmentconfiguration, often known as a “root”, “base” or “dovetail”.

The configuration of the airfoil and any interaction with surroundingairfoils, as embodied by the invention, that provide the desirableaspects fluid flow dynamics and laminar flow of the invention can bedetermined by various means. Fluid flow from a preceding/upstreamairfoil intersects with the airfoil, as embodied by the invention, andvia the configuration of the instant airfoil, flow over and around theairfoil, as embodied by the invention, is enhanced. In particular, thefluid dynamics and laminar flow from the airfoil, as embodied by theinvention, is enhanced. There is a smooth transition fluid flow from anypreceding/upstream airfoil(s) and a smooth transition fluid flow to theadjacent/downstream airfoil(s). Moreover, the flow from the airfoil, asembodied by the invention, proceeds to the adjacent/downstreamairfoil(s) is enhanced due to the enhanced laminar fluid flow off of theairfoil, as embodied by the invention. Therefore, the configuration ofthe airfoil, as embodied by the invention, assists in the prevention ofturbulent fluid flow in the unit comprising the airfoil, as embodied bythe invention.

For example, but in no way limiting of the invention, the airfoilconfiguration (with or without fluid flow interaction) can be determinedby computational modeling, Fluid Dynamics (CFD); traditional fluiddynamics analysis; Euler and Navier-Stokes equations; for transferfunctions, algorithms, manufacturing: manual positioning, flow testing(for example in wind tunnels), and modification of the airfoil; in-situtesting; modeling: application of scientific principles to design ordevelop the airfoils, machines, apparatus, or manufacturing processes;airfoil flow testing and modification; combinations thereof, and otherdesign processes and practices. These methods of determination aremerely exemplary, and are not intended to limit the invention in anymanner.

As noted above, the airfoil configuration (along with its interactionwith surrounding airfoils), as embodied by the invention, including itsperipheral surface provides for stage airflow efficiency, enhancedaeromechanics, smooth laminar flow from stage to stage, reduced thermalstresses, enhanced interrelation of the stages to effectively pass theairflow from stage to stage, and reduced mechanical stresses, amongother desirable aspects of the invention, compared to other similarairfoils, which have like applications. Of course, other such advantagesare within the scope of the invention.

While various embodiments are described herein, it will be appreciatedfrom the specification that various combinations of elements, variationsor improvements therein may be made by those skilled in the art, and arewithin the scope of the invention.

1. An article of manufacture, the article having a nominal profilesubstantially in accordance with Cartesian coordinate values of X, Y andZ set forth in TABLE A, and wherein X and Y are distances in incheswhich, when connected by smooth continuing arcs, define airfoil profilesections at each distance Z in inches, the profile sections at the Zdistances being joined smoothly with one another to form a completeairfoil shape.
 2. An article of manufacture according to claim 1,wherein the airfoil shape comprises an airfoil.
 3. An article ofmanufacture according to claim 2, wherein said airfoil shape lies in anenvelope within ±0.160 inches in a direction normal to any articlesurface location.
 4. An article of manufacture according to claim 1,wherein the airfoil shape comprises a rotor blade.
 5. A compressorcomprising a compressor wheel having a plurality of blades, each of saidblades cooperating with a plurality of rotor vanes, the plurality ofrotor vanes comprising an airfoil having an airfoil shape, said airfoilshape having a nominal profile substantially in accordance withCartesian coordinate values of X, Y and Z set forth in TABLE A, whereinX and Y are distances in inches which, when connected by smoothcontinuing arcs, define the airfoil profile sections at each distance Zin inches, the profile sections at the Z distances being joined smoothlywith one another to form a complete airfoil shape.
 6. A compressorcomprising a compressor wheel having a plurality of vanes, the pluralityof vanes comprising an airfoil having an uncoated nominal airfoilprofile substantially in accordance with Cartesian coordinate values ofX, Y and Z set forth in TABLE A, wherein X and Y are distances in incheswhich, when connected by smooth continuing arcs, define airfoil profilesections at each distance Z in inches, the profile sections at the Zdistances being joined smoothly with one another to form a completeairfoil shape, the X and Y distances being scalable as a function of thesame constant or number to provide at least one of a scaled up airfoiland scaled down airfoil.
 7. A compressor according to claim 6 whereinthe plurality of blades comprise a Stage 1 rotor vane.
 8. A compressoraccording to claim 6 wherein said airfoil shape lies in an envelopewithin ±0.160 inches in a direction normal to any airfoil surfacelocation.